One of the reasons Schumer is so popular is that she’s managed to transcend (or at least avoid) the “debate” around likeability that has plagued other female stars. The characters she plays on her show are so over the top that Schumer avoids the conflation of confected and real that has been applied – often unflatteringly – to Mindy Kaling and Mindy Lahiri, or Lena Dunham and Hannah Horvath, the role Dunham plays in Girls. Schumer’s drunk party slut persona has proven a safe jumping-off point for increasingly politically minded satire on the show, all the while appealing to Comedy Central’s largely male viewers with a classic trope: the hot girl with a potty mouth.

Although Schumer has made comic fodder of the idea that she’s not Hollywood-attractive – most notably in 12 Angry Men Inside Amy Schumer, an episode-long sketch in which Paul Giamatti, Jeff Goldblum and others debate whether or not she’s “hot enough to be on TV” – she’s still an attractive, blonde, white woman with blue eyes and a cute smile. In a 2012 Howard Stern interview, the comedian copped to wearing heels and a short dress for her standup special Mostly Sex Stuff, because “people see a female comedian and they’re just like, ‘Yawn, what else is on?’ But they see a chick that’s kind of interesting to look at and you see some skin, and at least you’ll stay tuned to see what she has to say.”

This keen awareness of the garbage women in the media have to put up with combined with a bro-y “let’s do some shots about it” attitude is what’s helped Schumer achieve something that’s long been presented as impossible: funny, feminist, mainstream entertainment.Feminism’s image has never been particularly fun, and as Emily Nussbaum at the New Yorker notes, “Can’t you take a joke?” has been the de facto defence of sexism for decades.

In her show and stand-up material, Schumer proves that she can, often making herself the butt of a joke in service of its wider goals. Here, too, she pulls off an impressive feat, as Nussbam elaborates: “Comedy with a message can also easily turn didactic – or, worse, smug. Luckily, Schumer’s show feels built to withstand this pressure, even as it expands its reach, touching on subjects like reproductive rights and equal pay.”

While Schumer’s politics are impressive, her jokes are just as much so; she has serious comedic clout in addition to a feminist agenda. Football Town Nights was a viral hit because of its incisive skewering of rape culture in the education system – but the sketch was also a hilarious parody of Friday Night Lightsand small town football movies in general, with Schumer playing a would-be Tammy Taylor, drunk off increasingly large glasses of white wine, asking her husband to tone it down with the no raping rule. Other Comedy Central offerings, like The Daily Show and The Colbert Report, can be steeped in “clapter” – a term invented by Seth Meyers to mean the hooting that accompanies political jokes the audience agrees with rather than finds amusing – instead of laughter. Schumer’s comedy delivers its message so successfully because at times you forget it’s being delivered at all.

But despite widespread praise, Inside Amy Schumer has suffered a smiilar fate to that of NBC’s Parks and Recreation: critical acclaim, low ratings. The first three episodes of Schumer’s third season averaged 881,000 viewers each. While more than three million online viewers saw her widely shared Girl, You Don’t Need Makeup sketch – a pitch-perfect parody of patronising boy band songs that insist they’re the only ones who can appreciate the real you – they did so for free on YouTube, experiencing Schumer’s show as a single sketch, not a complete product.

Viewers taking the greatest hits-style YouTube approach to Schumer’s show would have missed, then, a sketch where a hapless Amy, desperate to fit in with the guys at work, helps them bury a stripper they killed. As the men walk away, the stripper begins to stir, and Amy, alone, hits her over the head with a shovel. Or Fight Like a Girl, a sketch in which Amy turns sensei to a group of men hoping to outwit their girlfriends in “female emotional combat”. The sketch isn’t unfunny, but it’s not the boundary-pushing fare viewers associate with Schumer, and the jokes tread territory (“women be crazy”) that is at best old hat and at worst, classically misogynist. Clips-only viewers might also have missed The Problem With Urban Outfitters, a sketch in which the titular problem appears to be that all the store’s black employees look the same.

For such a keen observer of social norms and an effective satirist of the ways gender is complicated by them, Schumer has a shockingly large blind spot around race. Her lacklustre stint hosting the MTV Movie awards (a rare misstep) featured lazy jokes about Latina women being “crazy” that left Jennifer Lopez as unimpressed as the online commentariat. While a much-lauded sketch from the show featured an ad for a training centre where old people learn not to be racist, Schumer’s stand-up repeatedly delves into racial territory tactlessly and with no apparent larger point. Her standup special features jokes like“Nothing works 100% of the time, except Mexicans” and much of her character’s dumb slut persona is predicated on the fact that the men she sleeps with are people of colour. “I used to date Latino guys,” she says in an older stand-up routine. “Now I prefer consensual.”

Schumer has said that she’s not worried about the show upsetting people because viewers know “we have good intentions”, but as Anne Thériault wrote for the Daily Dot: “Amy Schumer frequently makes jokes that perpetuate stereotypes rather than dismantle them … It’s hard not to feel like Schumer is only here for women who look like her.”

While there’s no denying that Schumer is an incredible talent, the material that doesn’t make the next morning’s feminist Facebook shares doesn’t fare quite so well under scrutiny. And perhaps a Schumer backlash is inevitable. Still, her widespread popularity and apparently endlessly rising star suggests that Schumer is providing something we’ve been hungry for: a walking, talking, occasionally farting counter-argument to the idea that feminists aren’t funny.

Amy Schumer responded on Sunday via Twitter to allegations of a racial blind spot in her comedy, writing: “Stick with me and trust me that I’m joking. I go in and out of playing an irreverent idiot. That includes making dumb jokes involving race …You can call it a “blind spot for racism” or “lazy” but you are wrong. It is a joke and it is funny … I am not going to start joking about safe material.”